Properties

Label 690.2.i.f.47.7
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.7
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.12660 - 1.31559i) q^{3} -1.00000i q^{4} +(-0.192443 + 2.22777i) q^{5} +(0.133641 + 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.461565 - 2.96428i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.12660 - 1.31559i) q^{3} -1.00000i q^{4} +(-0.192443 + 2.22777i) q^{5} +(0.133641 + 1.72689i) q^{6} +(1.96010 + 1.96010i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.461565 - 2.96428i) q^{9} +(-1.43919 - 1.71135i) q^{10} +2.97195i q^{11} +(-1.31559 - 1.12660i) q^{12} +(-1.33263 + 1.33263i) q^{13} -2.77200 q^{14} +(2.71403 + 2.76297i) q^{15} -1.00000 q^{16} +(0.217329 - 0.217329i) q^{17} +(2.42244 + 1.76969i) q^{18} +6.42606i q^{19} +(2.22777 + 0.192443i) q^{20} +(4.78694 - 0.370453i) q^{21} +(-2.10149 - 2.10149i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.72689 - 0.133641i) q^{24} +(-4.92593 - 0.857436i) q^{25} -1.88462i q^{26} +(-4.41978 - 2.73231i) q^{27} +(1.96010 - 1.96010i) q^{28} -1.22002 q^{29} +(-3.87283 - 0.0346053i) q^{30} +6.33502 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.90988 + 3.34819i) q^{33} +0.307349i q^{34} +(-4.74387 + 3.98945i) q^{35} +(-2.96428 + 0.461565i) q^{36} +(1.43305 + 1.43305i) q^{37} +(-4.54391 - 4.54391i) q^{38} +(0.251863 + 3.25453i) q^{39} +(-1.71135 + 1.43919i) q^{40} -3.04579i q^{41} +(-3.12292 + 3.64682i) q^{42} +(-1.80190 + 1.80190i) q^{43} +2.97195 q^{44} +(6.69256 - 0.457809i) q^{45} +1.00000 q^{46} +(0.199419 - 0.199419i) q^{47} +(-1.12660 + 1.31559i) q^{48} +0.683996i q^{49} +(4.08946 - 2.87686i) q^{50} +(-0.0410744 - 0.530758i) q^{51} +(1.33263 + 1.33263i) q^{52} +(9.17886 + 9.17886i) q^{53} +(5.05729 - 1.19322i) q^{54} +(-6.62083 - 0.571930i) q^{55} +2.77200i q^{56} +(8.45408 + 7.23957i) q^{57} +(0.862686 - 0.862686i) q^{58} +9.43000 q^{59} +(2.76297 - 2.71403i) q^{60} +5.57225 q^{61} +(-4.47954 + 4.47954i) q^{62} +(4.90558 - 6.71501i) q^{63} +1.00000i q^{64} +(-2.71234 - 3.22525i) q^{65} +(-5.13223 + 0.397175i) q^{66} +(9.41060 + 9.41060i) q^{67} +(-0.217329 - 0.217329i) q^{68} +(-1.72689 + 0.133641i) q^{69} +(0.533451 - 6.17539i) q^{70} -7.64983i q^{71} +(1.76969 - 2.42244i) q^{72} +(-4.05708 + 4.05708i) q^{73} -2.02664 q^{74} +(-6.67757 + 5.51453i) q^{75} +6.42606 q^{76} +(-5.82533 + 5.82533i) q^{77} +(-2.47940 - 2.12321i) q^{78} -14.4298i q^{79} +(0.192443 - 2.22777i) q^{80} +(-8.57391 + 2.73642i) q^{81} +(2.15370 + 2.15370i) q^{82} +(-12.1736 - 12.1736i) q^{83} +(-0.370453 - 4.78694i) q^{84} +(0.442336 + 0.525982i) q^{85} -2.54827i q^{86} +(-1.37447 + 1.60505i) q^{87} +(-2.10149 + 2.10149i) q^{88} -2.45643 q^{89} +(-4.40864 + 5.05608i) q^{90} -5.22418 q^{91} +(-0.707107 + 0.707107i) q^{92} +(7.13701 - 8.33431i) q^{93} +0.282021i q^{94} +(-14.3158 - 1.23665i) q^{95} +(-0.133641 - 1.72689i) q^{96} +(8.98748 + 8.98748i) q^{97} +(-0.483658 - 0.483658i) q^{98} +(8.80970 - 1.37175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.12660 1.31559i 0.650440 0.759557i
\(4\) 1.00000i 0.500000i
\(5\) −0.192443 + 2.22777i −0.0860629 + 0.996290i
\(6\) 0.133641 + 1.72689i 0.0545587 + 0.704999i
\(7\) 1.96010 + 1.96010i 0.740849 + 0.740849i 0.972741 0.231893i \(-0.0744918\pi\)
−0.231893 + 0.972741i \(0.574492\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −0.461565 2.96428i −0.153855 0.988093i
\(10\) −1.43919 1.71135i −0.455113 0.541176i
\(11\) 2.97195i 0.896078i 0.894014 + 0.448039i \(0.147877\pi\)
−0.894014 + 0.448039i \(0.852123\pi\)
\(12\) −1.31559 1.12660i −0.379779 0.325220i
\(13\) −1.33263 + 1.33263i −0.369605 + 0.369605i −0.867333 0.497728i \(-0.834168\pi\)
0.497728 + 0.867333i \(0.334168\pi\)
\(14\) −2.77200 −0.740849
\(15\) 2.71403 + 2.76297i 0.700761 + 0.713397i
\(16\) −1.00000 −0.250000
\(17\) 0.217329 0.217329i 0.0527100 0.0527100i −0.680260 0.732970i \(-0.738133\pi\)
0.732970 + 0.680260i \(0.238133\pi\)
\(18\) 2.42244 + 1.76969i 0.570974 + 0.417119i
\(19\) 6.42606i 1.47424i 0.675762 + 0.737120i \(0.263815\pi\)
−0.675762 + 0.737120i \(0.736185\pi\)
\(20\) 2.22777 + 0.192443i 0.498145 + 0.0430315i
\(21\) 4.78694 0.370453i 1.04459 0.0808394i
\(22\) −2.10149 2.10149i −0.448039 0.448039i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) 1.72689 0.133641i 0.352499 0.0272793i
\(25\) −4.92593 0.857436i −0.985186 0.171487i
\(26\) 1.88462i 0.369605i
\(27\) −4.41978 2.73231i −0.850587 0.525834i
\(28\) 1.96010 1.96010i 0.370424 0.370424i
\(29\) −1.22002 −0.226552 −0.113276 0.993564i \(-0.536134\pi\)
−0.113276 + 0.993564i \(0.536134\pi\)
\(30\) −3.87283 0.0346053i −0.707079 0.00631804i
\(31\) 6.33502 1.13780 0.568902 0.822405i \(-0.307368\pi\)
0.568902 + 0.822405i \(0.307368\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 3.90988 + 3.34819i 0.680623 + 0.582845i
\(34\) 0.307349i 0.0527100i
\(35\) −4.74387 + 3.98945i −0.801860 + 0.674340i
\(36\) −2.96428 + 0.461565i −0.494047 + 0.0769276i
\(37\) 1.43305 + 1.43305i 0.235592 + 0.235592i 0.815022 0.579430i \(-0.196725\pi\)
−0.579430 + 0.815022i \(0.696725\pi\)
\(38\) −4.54391 4.54391i −0.737120 0.737120i
\(39\) 0.251863 + 3.25453i 0.0403303 + 0.521142i
\(40\) −1.71135 + 1.43919i −0.270588 + 0.227557i
\(41\) 3.04579i 0.475672i −0.971305 0.237836i \(-0.923562\pi\)
0.971305 0.237836i \(-0.0764380\pi\)
\(42\) −3.12292 + 3.64682i −0.481878 + 0.562717i
\(43\) −1.80190 + 1.80190i −0.274786 + 0.274786i −0.831024 0.556237i \(-0.812245\pi\)
0.556237 + 0.831024i \(0.312245\pi\)
\(44\) 2.97195 0.448039
\(45\) 6.69256 0.457809i 0.997669 0.0682461i
\(46\) 1.00000 0.147442
\(47\) 0.199419 0.199419i 0.0290883 0.0290883i −0.692413 0.721501i \(-0.743452\pi\)
0.721501 + 0.692413i \(0.243452\pi\)
\(48\) −1.12660 + 1.31559i −0.162610 + 0.189889i
\(49\) 0.683996i 0.0977137i
\(50\) 4.08946 2.87686i 0.578337 0.406850i
\(51\) −0.0410744 0.530758i −0.00575157 0.0743210i
\(52\) 1.33263 + 1.33263i 0.184803 + 0.184803i
\(53\) 9.17886 + 9.17886i 1.26081 + 1.26081i 0.950699 + 0.310114i \(0.100367\pi\)
0.310114 + 0.950699i \(0.399633\pi\)
\(54\) 5.05729 1.19322i 0.688211 0.162377i
\(55\) −6.62083 0.571930i −0.892753 0.0771191i
\(56\) 2.77200i 0.370424i
\(57\) 8.45408 + 7.23957i 1.11977 + 0.958905i
\(58\) 0.862686 0.862686i 0.113276 0.113276i
\(59\) 9.43000 1.22768 0.613841 0.789430i \(-0.289624\pi\)
0.613841 + 0.789430i \(0.289624\pi\)
\(60\) 2.76297 2.71403i 0.356698 0.350380i
\(61\) 5.57225 0.713454 0.356727 0.934209i \(-0.383893\pi\)
0.356727 + 0.934209i \(0.383893\pi\)
\(62\) −4.47954 + 4.47954i −0.568902 + 0.568902i
\(63\) 4.90558 6.71501i 0.618044 0.846011i
\(64\) 1.00000i 0.125000i
\(65\) −2.71234 3.22525i −0.336425 0.400043i
\(66\) −5.13223 + 0.397175i −0.631734 + 0.0488888i
\(67\) 9.41060 + 9.41060i 1.14969 + 1.14969i 0.986614 + 0.163074i \(0.0521410\pi\)
0.163074 + 0.986614i \(0.447859\pi\)
\(68\) −0.217329 0.217329i −0.0263550 0.0263550i
\(69\) −1.72689 + 0.133641i −0.207893 + 0.0160885i
\(70\) 0.533451 6.17539i 0.0637596 0.738100i
\(71\) 7.64983i 0.907868i −0.891035 0.453934i \(-0.850020\pi\)
0.891035 0.453934i \(-0.149980\pi\)
\(72\) 1.76969 2.42244i 0.208560 0.285487i
\(73\) −4.05708 + 4.05708i −0.474845 + 0.474845i −0.903479 0.428633i \(-0.858995\pi\)
0.428633 + 0.903479i \(0.358995\pi\)
\(74\) −2.02664 −0.235592
\(75\) −6.67757 + 5.51453i −0.771059 + 0.636763i
\(76\) 6.42606 0.737120
\(77\) −5.82533 + 5.82533i −0.663858 + 0.663858i
\(78\) −2.47940 2.12321i −0.280736 0.240406i
\(79\) 14.4298i 1.62348i −0.584018 0.811741i \(-0.698520\pi\)
0.584018 0.811741i \(-0.301480\pi\)
\(80\) 0.192443 2.22777i 0.0215157 0.249072i
\(81\) −8.57391 + 2.73642i −0.952657 + 0.304047i
\(82\) 2.15370 + 2.15370i 0.237836 + 0.237836i
\(83\) −12.1736 12.1736i −1.33622 1.33622i −0.899688 0.436533i \(-0.856206\pi\)
−0.436533 0.899688i \(-0.643794\pi\)
\(84\) −0.370453 4.78694i −0.0404197 0.522297i
\(85\) 0.442336 + 0.525982i 0.0479780 + 0.0570508i
\(86\) 2.54827i 0.274786i
\(87\) −1.37447 + 1.60505i −0.147359 + 0.172080i
\(88\) −2.10149 + 2.10149i −0.224019 + 0.224019i
\(89\) −2.45643 −0.260381 −0.130191 0.991489i \(-0.541559\pi\)
−0.130191 + 0.991489i \(0.541559\pi\)
\(90\) −4.40864 + 5.05608i −0.464711 + 0.532957i
\(91\) −5.22418 −0.547643
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 7.13701 8.33431i 0.740073 0.864227i
\(94\) 0.282021i 0.0290883i
\(95\) −14.3158 1.23665i −1.46877 0.126877i
\(96\) −0.133641 1.72689i −0.0136397 0.176250i
\(97\) 8.98748 + 8.98748i 0.912541 + 0.912541i 0.996472 0.0839309i \(-0.0267475\pi\)
−0.0839309 + 0.996472i \(0.526748\pi\)
\(98\) −0.483658 0.483658i −0.0488568 0.0488568i
\(99\) 8.80970 1.37175i 0.885409 0.137866i
\(100\) −0.857436 + 4.92593i −0.0857436 + 0.492593i
\(101\) 3.00976i 0.299482i −0.988725 0.149741i \(-0.952156\pi\)
0.988725 0.149741i \(-0.0478440\pi\)
\(102\) 0.404346 + 0.346258i 0.0400363 + 0.0342847i
\(103\) −1.81831 + 1.81831i −0.179163 + 0.179163i −0.790991 0.611828i \(-0.790435\pi\)
0.611828 + 0.790991i \(0.290435\pi\)
\(104\) −1.88462 −0.184803
\(105\) −0.0959261 + 10.7355i −0.00936143 + 1.04768i
\(106\) −12.9809 −1.26081
\(107\) −10.1552 + 10.1552i −0.981744 + 0.981744i −0.999836 0.0180921i \(-0.994241\pi\)
0.0180921 + 0.999836i \(0.494241\pi\)
\(108\) −2.73231 + 4.41978i −0.262917 + 0.425294i
\(109\) 3.22282i 0.308690i −0.988017 0.154345i \(-0.950673\pi\)
0.988017 0.154345i \(-0.0493268\pi\)
\(110\) 5.08605 4.27722i 0.484936 0.407817i
\(111\) 3.49978 0.270842i 0.332184 0.0257072i
\(112\) −1.96010 1.96010i −0.185212 0.185212i
\(113\) −3.72990 3.72990i −0.350880 0.350880i 0.509557 0.860437i \(-0.329809\pi\)
−0.860437 + 0.509557i \(0.829809\pi\)
\(114\) −11.0971 + 0.858785i −1.03934 + 0.0804326i
\(115\) 1.71135 1.43919i 0.159584 0.134206i
\(116\) 1.22002i 0.113276i
\(117\) 4.56539 + 3.33519i 0.422070 + 0.308339i
\(118\) −6.66802 + 6.66802i −0.613841 + 0.613841i
\(119\) 0.851973 0.0781003
\(120\) −0.0346053 + 3.87283i −0.00315902 + 0.353539i
\(121\) 2.16749 0.197044
\(122\) −3.94018 + 3.94018i −0.356727 + 0.356727i
\(123\) −4.00701 3.43137i −0.361300 0.309396i
\(124\) 6.33502i 0.568902i
\(125\) 2.85813 10.8088i 0.255639 0.966772i
\(126\) 1.27946 + 8.21699i 0.113983 + 0.732028i
\(127\) −9.95020 9.95020i −0.882938 0.882938i 0.110895 0.993832i \(-0.464628\pi\)
−0.993832 + 0.110895i \(0.964628\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 0.340552 + 4.40057i 0.0299840 + 0.387448i
\(130\) 4.19851 + 0.362682i 0.368234 + 0.0318093i
\(131\) 4.14724i 0.362346i −0.983451 0.181173i \(-0.942011\pi\)
0.983451 0.181173i \(-0.0579894\pi\)
\(132\) 3.34819 3.90988i 0.291423 0.340311i
\(133\) −12.5957 + 12.5957i −1.09219 + 1.09219i
\(134\) −13.3086 −1.14969
\(135\) 6.93752 9.32045i 0.597087 0.802177i
\(136\) 0.307349 0.0263550
\(137\) 6.71805 6.71805i 0.573962 0.573962i −0.359271 0.933233i \(-0.616975\pi\)
0.933233 + 0.359271i \(0.116975\pi\)
\(138\) 1.12660 1.31559i 0.0959022 0.111991i
\(139\) 21.3303i 1.80921i −0.426247 0.904607i \(-0.640165\pi\)
0.426247 0.904607i \(-0.359835\pi\)
\(140\) 3.98945 + 4.74387i 0.337170 + 0.400930i
\(141\) −0.0376896 0.487019i −0.00317404 0.0410144i
\(142\) 5.40925 + 5.40925i 0.453934 + 0.453934i
\(143\) −3.96052 3.96052i −0.331195 0.331195i
\(144\) 0.461565 + 2.96428i 0.0384638 + 0.247023i
\(145\) 0.234784 2.71793i 0.0194978 0.225712i
\(146\) 5.73758i 0.474845i
\(147\) 0.899860 + 0.770587i 0.0742192 + 0.0635569i
\(148\) 1.43305 1.43305i 0.117796 0.117796i
\(149\) 2.04707 0.167703 0.0838514 0.996478i \(-0.473278\pi\)
0.0838514 + 0.996478i \(0.473278\pi\)
\(150\) 0.822390 8.62112i 0.0671479 0.703911i
\(151\) −2.64015 −0.214852 −0.107426 0.994213i \(-0.534261\pi\)
−0.107426 + 0.994213i \(0.534261\pi\)
\(152\) −4.54391 + 4.54391i −0.368560 + 0.368560i
\(153\) −0.744535 0.543912i −0.0601921 0.0439727i
\(154\) 8.23826i 0.663858i
\(155\) −1.21913 + 14.1130i −0.0979227 + 1.13358i
\(156\) 3.25453 0.251863i 0.260571 0.0201652i
\(157\) 0.750993 + 0.750993i 0.0599358 + 0.0599358i 0.736439 0.676504i \(-0.236506\pi\)
−0.676504 + 0.736439i \(0.736506\pi\)
\(158\) 10.2034 + 10.2034i 0.811741 + 0.811741i
\(159\) 22.4165 1.73477i 1.77774 0.137577i
\(160\) 1.43919 + 1.71135i 0.113778 + 0.135294i
\(161\) 2.77200i 0.218464i
\(162\) 4.12773 7.99761i 0.324305 0.628352i
\(163\) 6.60415 6.60415i 0.517277 0.517277i −0.399469 0.916747i \(-0.630806\pi\)
0.916747 + 0.399469i \(0.130806\pi\)
\(164\) −3.04579 −0.237836
\(165\) −8.21143 + 8.06598i −0.639259 + 0.627936i
\(166\) 17.2160 1.33622
\(167\) 5.25056 5.25056i 0.406300 0.406300i −0.474146 0.880446i \(-0.657243\pi\)
0.880446 + 0.474146i \(0.157243\pi\)
\(168\) 3.64682 + 3.12292i 0.281359 + 0.240939i
\(169\) 9.44819i 0.726784i
\(170\) −0.684704 0.0591471i −0.0525144 0.00453638i
\(171\) 19.0487 2.96605i 1.45669 0.226819i
\(172\) 1.80190 + 1.80190i 0.137393 + 0.137393i
\(173\) −16.1787 16.1787i −1.23004 1.23004i −0.963947 0.266093i \(-0.914267\pi\)
−0.266093 0.963947i \(-0.585733\pi\)
\(174\) −0.163045 2.10684i −0.0123604 0.159719i
\(175\) −7.97466 11.3360i −0.602828 0.856920i
\(176\) 2.97195i 0.224019i
\(177\) 10.6238 12.4060i 0.798533 0.932495i
\(178\) 1.73696 1.73696i 0.130191 0.130191i
\(179\) 12.6087 0.942418 0.471209 0.882022i \(-0.343818\pi\)
0.471209 + 0.882022i \(0.343818\pi\)
\(180\) −0.457809 6.69256i −0.0341230 0.498834i
\(181\) −1.75381 −0.130360 −0.0651799 0.997874i \(-0.520762\pi\)
−0.0651799 + 0.997874i \(0.520762\pi\)
\(182\) 3.69405 3.69405i 0.273822 0.273822i
\(183\) 6.27767 7.33081i 0.464059 0.541909i
\(184\) 1.00000i 0.0737210i
\(185\) −3.46829 + 2.91673i −0.254994 + 0.214442i
\(186\) 0.846618 + 10.9399i 0.0620771 + 0.802150i
\(187\) 0.645891 + 0.645891i 0.0472322 + 0.0472322i
\(188\) −0.199419 0.199419i −0.0145441 0.0145441i
\(189\) −3.30761 14.0188i −0.240593 1.01972i
\(190\) 10.9972 9.24836i 0.797824 0.670946i
\(191\) 26.9285i 1.94848i −0.225520 0.974238i \(-0.572408\pi\)
0.225520 0.974238i \(-0.427592\pi\)
\(192\) 1.31559 + 1.12660i 0.0949447 + 0.0813050i
\(193\) −10.9317 + 10.9317i −0.786878 + 0.786878i −0.980981 0.194103i \(-0.937820\pi\)
0.194103 + 0.980981i \(0.437820\pi\)
\(194\) −12.7102 −0.912541
\(195\) −7.29883 0.0652180i −0.522680 0.00467036i
\(196\) 0.683996 0.0488568
\(197\) −1.97929 + 1.97929i −0.141019 + 0.141019i −0.774092 0.633073i \(-0.781793\pi\)
0.633073 + 0.774092i \(0.281793\pi\)
\(198\) −5.25943 + 7.19938i −0.373771 + 0.511637i
\(199\) 15.8892i 1.12636i −0.826336 0.563178i \(-0.809579\pi\)
0.826336 0.563178i \(-0.190421\pi\)
\(200\) −2.87686 4.08946i −0.203425 0.289168i
\(201\) 22.9825 1.77857i 1.62106 0.125451i
\(202\) 2.12822 + 2.12822i 0.149741 + 0.149741i
\(203\) −2.39137 2.39137i −0.167841 0.167841i
\(204\) −0.530758 + 0.0410744i −0.0371605 + 0.00287579i
\(205\) 6.78531 + 0.586139i 0.473907 + 0.0409377i
\(206\) 2.57147i 0.179163i
\(207\) −1.76969 + 2.42244i −0.123002 + 0.168371i
\(208\) 1.33263 1.33263i 0.0924013 0.0924013i
\(209\) −19.0980 −1.32103
\(210\) −7.52331 7.65897i −0.519158 0.528519i
\(211\) 11.3907 0.784169 0.392085 0.919929i \(-0.371754\pi\)
0.392085 + 0.919929i \(0.371754\pi\)
\(212\) 9.17886 9.17886i 0.630407 0.630407i
\(213\) −10.0641 8.61826i −0.689578 0.590514i
\(214\) 14.3617i 0.981744i
\(215\) −3.66745 4.36097i −0.250118 0.297416i
\(216\) −1.19322 5.05729i −0.0811884 0.344105i
\(217\) 12.4173 + 12.4173i 0.842941 + 0.842941i
\(218\) 2.27888 + 2.27888i 0.154345 + 0.154345i
\(219\) 0.766775 + 9.90815i 0.0518138 + 0.669531i
\(220\) −0.571930 + 6.62083i −0.0385595 + 0.446377i
\(221\) 0.579238i 0.0389638i
\(222\) −2.28320 + 2.66623i −0.153239 + 0.178946i
\(223\) −10.4680 + 10.4680i −0.700989 + 0.700989i −0.964623 0.263634i \(-0.915079\pi\)
0.263634 + 0.964623i \(0.415079\pi\)
\(224\) 2.77200 0.185212
\(225\) −0.268041 + 14.9976i −0.0178694 + 0.999840i
\(226\) 5.27488 0.350880
\(227\) −16.1663 + 16.1663i −1.07299 + 1.07299i −0.0758747 + 0.997117i \(0.524175\pi\)
−0.997117 + 0.0758747i \(0.975825\pi\)
\(228\) 7.23957 8.45408i 0.479453 0.559885i
\(229\) 16.0298i 1.05928i −0.848224 0.529638i \(-0.822328\pi\)
0.848224 0.529638i \(-0.177672\pi\)
\(230\) −0.192443 + 2.22777i −0.0126893 + 0.146895i
\(231\) 1.10097 + 14.2266i 0.0724384 + 0.936038i
\(232\) −0.862686 0.862686i −0.0566381 0.0566381i
\(233\) −4.14654 4.14654i −0.271649 0.271649i 0.558115 0.829764i \(-0.311525\pi\)
−0.829764 + 0.558115i \(0.811525\pi\)
\(234\) −5.58655 + 0.869877i −0.365204 + 0.0568657i
\(235\) 0.405884 + 0.482637i 0.0264769 + 0.0314838i
\(236\) 9.43000i 0.613841i
\(237\) −18.9838 16.2566i −1.23313 1.05598i
\(238\) −0.602436 + 0.602436i −0.0390501 + 0.0390501i
\(239\) 29.7656 1.92538 0.962690 0.270608i \(-0.0872246\pi\)
0.962690 + 0.270608i \(0.0872246\pi\)
\(240\) −2.71403 2.76297i −0.175190 0.178349i
\(241\) −18.1553 −1.16949 −0.584743 0.811219i \(-0.698805\pi\)
−0.584743 + 0.811219i \(0.698805\pi\)
\(242\) −1.53265 + 1.53265i −0.0985222 + 0.0985222i
\(243\) −6.05932 + 14.3626i −0.388706 + 0.921362i
\(244\) 5.57225i 0.356727i
\(245\) −1.52379 0.131630i −0.0973512 0.00840953i
\(246\) 5.25973 0.407041i 0.335348 0.0259520i
\(247\) −8.56357 8.56357i −0.544887 0.544887i
\(248\) 4.47954 + 4.47954i 0.284451 + 0.284451i
\(249\) −29.7301 + 2.30076i −1.88407 + 0.145805i
\(250\) 5.62200 + 9.66401i 0.355567 + 0.611206i
\(251\) 19.1213i 1.20693i 0.797390 + 0.603464i \(0.206213\pi\)
−0.797390 + 0.603464i \(0.793787\pi\)
\(252\) −6.71501 4.90558i −0.423006 0.309022i
\(253\) 2.10149 2.10149i 0.132119 0.132119i
\(254\) 14.0717 0.882938
\(255\) 1.19031 + 0.0106359i 0.0745402 + 0.000666048i
\(256\) 1.00000 0.0625000
\(257\) 17.0084 17.0084i 1.06096 1.06096i 0.0629387 0.998017i \(-0.479953\pi\)
0.998017 0.0629387i \(-0.0200473\pi\)
\(258\) −3.35248 2.87086i −0.208716 0.178732i
\(259\) 5.61785i 0.349076i
\(260\) −3.22525 + 2.71234i −0.200022 + 0.168212i
\(261\) 0.563120 + 3.61649i 0.0348563 + 0.223855i
\(262\) 2.93254 + 2.93254i 0.181173 + 0.181173i
\(263\) 12.3574 + 12.3574i 0.761992 + 0.761992i 0.976682 0.214690i \(-0.0688741\pi\)
−0.214690 + 0.976682i \(0.568874\pi\)
\(264\) 0.397175 + 5.13223i 0.0244444 + 0.315867i
\(265\) −22.2148 + 18.6820i −1.36464 + 1.14763i
\(266\) 17.8131i 1.09219i
\(267\) −2.76740 + 3.23166i −0.169362 + 0.197774i
\(268\) 9.41060 9.41060i 0.574844 0.574844i
\(269\) 20.0999 1.22552 0.612758 0.790271i \(-0.290060\pi\)
0.612758 + 0.790271i \(0.290060\pi\)
\(270\) 1.68498 + 11.4961i 0.102545 + 0.699632i
\(271\) −27.8676 −1.69284 −0.846419 0.532518i \(-0.821246\pi\)
−0.846419 + 0.532518i \(0.821246\pi\)
\(272\) −0.217329 + 0.217329i −0.0131775 + 0.0131775i
\(273\) −5.88554 + 6.87289i −0.356209 + 0.415966i
\(274\) 9.50076i 0.573962i
\(275\) 2.54826 14.6396i 0.153666 0.882804i
\(276\) 0.133641 + 1.72689i 0.00804423 + 0.103946i
\(277\) 7.04930 + 7.04930i 0.423551 + 0.423551i 0.886424 0.462873i \(-0.153182\pi\)
−0.462873 + 0.886424i \(0.653182\pi\)
\(278\) 15.0828 + 15.0828i 0.904607 + 0.904607i
\(279\) −2.92403 18.7788i −0.175057 1.12426i
\(280\) −6.17539 0.533451i −0.369050 0.0318798i
\(281\) 15.7886i 0.941867i 0.882169 + 0.470934i \(0.156083\pi\)
−0.882169 + 0.470934i \(0.843917\pi\)
\(282\) 0.371025 + 0.317724i 0.0220942 + 0.0189202i
\(283\) 13.2043 13.2043i 0.784912 0.784912i −0.195743 0.980655i \(-0.562712\pi\)
0.980655 + 0.195743i \(0.0627118\pi\)
\(284\) −7.64983 −0.453934
\(285\) −17.7550 + 17.4406i −1.05172 + 1.03309i
\(286\) 5.60102 0.331195
\(287\) 5.97005 5.97005i 0.352401 0.352401i
\(288\) −2.42244 1.76969i −0.142744 0.104280i
\(289\) 16.9055i 0.994443i
\(290\) 1.75585 + 2.08788i 0.103107 + 0.122605i
\(291\) 21.9491 1.69860i 1.28668 0.0995740i
\(292\) 4.05708 + 4.05708i 0.237423 + 0.237423i
\(293\) 6.93824 + 6.93824i 0.405336 + 0.405336i 0.880109 0.474772i \(-0.157470\pi\)
−0.474772 + 0.880109i \(0.657470\pi\)
\(294\) −1.18118 + 0.0914098i −0.0688880 + 0.00533113i
\(295\) −1.81473 + 21.0079i −0.105658 + 1.22313i
\(296\) 2.02664i 0.117796i
\(297\) 8.12031 13.1354i 0.471188 0.762192i
\(298\) −1.44750 + 1.44750i −0.0838514 + 0.0838514i
\(299\) 1.88462 0.108991
\(300\) 5.51453 + 6.67757i 0.318382 + 0.385530i
\(301\) −7.06380 −0.407150
\(302\) 1.86687 1.86687i 0.107426 0.107426i
\(303\) −3.95962 3.39078i −0.227474 0.194795i
\(304\) 6.42606i 0.368560i
\(305\) −1.07234 + 12.4137i −0.0614019 + 0.710807i
\(306\) 0.911070 0.141862i 0.0520824 0.00810970i
\(307\) −8.38939 8.38939i −0.478808 0.478808i 0.425943 0.904750i \(-0.359943\pi\)
−0.904750 + 0.425943i \(0.859943\pi\)
\(308\) 5.82533 + 5.82533i 0.331929 + 0.331929i
\(309\) 0.343654 + 4.44065i 0.0195498 + 0.252620i
\(310\) −9.11733 10.8414i −0.517830 0.615753i
\(311\) 22.7094i 1.28773i 0.765139 + 0.643865i \(0.222670\pi\)
−0.765139 + 0.643865i \(0.777330\pi\)
\(312\) −2.12321 + 2.47940i −0.120203 + 0.140368i
\(313\) −19.0911 + 19.0911i −1.07909 + 1.07909i −0.0825035 + 0.996591i \(0.526292\pi\)
−0.996591 + 0.0825035i \(0.973708\pi\)
\(314\) −1.06206 −0.0599358
\(315\) 14.0155 + 12.2208i 0.789681 + 0.688561i
\(316\) −14.4298 −0.811741
\(317\) −0.0275450 + 0.0275450i −0.00154708 + 0.00154708i −0.707880 0.706333i \(-0.750348\pi\)
0.706333 + 0.707880i \(0.250348\pi\)
\(318\) −14.6242 + 17.0775i −0.820084 + 0.957660i
\(319\) 3.62585i 0.203009i
\(320\) −2.22777 0.192443i −0.124536 0.0107579i
\(321\) 1.91931 + 24.8010i 0.107125 + 1.38426i
\(322\) 1.96010 + 1.96010i 0.109232 + 0.109232i
\(323\) 1.39657 + 1.39657i 0.0777072 + 0.0777072i
\(324\) 2.73642 + 8.57391i 0.152023 + 0.476329i
\(325\) 7.70709 5.42180i 0.427513 0.300747i
\(326\) 9.33968i 0.517277i
\(327\) −4.23992 3.63082i −0.234468 0.200785i
\(328\) 2.15370 2.15370i 0.118918 0.118918i
\(329\) 0.781764 0.0431000
\(330\) 0.102845 11.5099i 0.00566146 0.633597i
\(331\) 1.05162 0.0578024 0.0289012 0.999582i \(-0.490799\pi\)
0.0289012 + 0.999582i \(0.490799\pi\)
\(332\) −12.1736 + 12.1736i −0.668111 + 0.668111i
\(333\) 3.58652 4.90941i 0.196540 0.269034i
\(334\) 7.42541i 0.406300i
\(335\) −22.7757 + 19.1537i −1.24437 + 1.04648i
\(336\) −4.78694 + 0.370453i −0.261149 + 0.0202099i
\(337\) −10.0242 10.0242i −0.546054 0.546054i 0.379243 0.925297i \(-0.376184\pi\)
−0.925297 + 0.379243i \(0.876184\pi\)
\(338\) −6.68088 6.68088i −0.363392 0.363392i
\(339\) −9.10912 + 0.704939i −0.494740 + 0.0382871i
\(340\) 0.525982 0.442336i 0.0285254 0.0239890i
\(341\) 18.8274i 1.01956i
\(342\) −11.3721 + 15.5667i −0.614934 + 0.841753i
\(343\) 12.3800 12.3800i 0.668458 0.668458i
\(344\) −2.54827 −0.137393
\(345\) 0.0346053 3.87283i 0.00186309 0.208506i
\(346\) 22.8801 1.23004
\(347\) 18.2887 18.2887i 0.981790 0.981790i −0.0180467 0.999837i \(-0.505745\pi\)
0.999837 + 0.0180467i \(0.00574476\pi\)
\(348\) 1.60505 + 1.37447i 0.0860398 + 0.0736794i
\(349\) 28.7041i 1.53649i −0.640154 0.768247i \(-0.721129\pi\)
0.640154 0.768247i \(-0.278871\pi\)
\(350\) 13.6547 + 2.37681i 0.729874 + 0.127046i
\(351\) 9.53110 2.24877i 0.508732 0.120031i
\(352\) 2.10149 + 2.10149i 0.112010 + 0.112010i
\(353\) 10.4582 + 10.4582i 0.556631 + 0.556631i 0.928347 0.371715i \(-0.121230\pi\)
−0.371715 + 0.928347i \(0.621230\pi\)
\(354\) 1.26023 + 16.2846i 0.0669807 + 0.865514i
\(355\) 17.0421 + 1.47215i 0.904499 + 0.0781337i
\(356\) 2.45643i 0.130191i
\(357\) 0.959829 1.12085i 0.0507995 0.0593216i
\(358\) −8.91569 + 8.91569i −0.471209 + 0.471209i
\(359\) −10.4419 −0.551105 −0.275552 0.961286i \(-0.588861\pi\)
−0.275552 + 0.961286i \(0.588861\pi\)
\(360\) 5.05608 + 4.40864i 0.266479 + 0.232356i
\(361\) −22.2943 −1.17338
\(362\) 1.24013 1.24013i 0.0651799 0.0651799i
\(363\) 2.44188 2.85153i 0.128166 0.149667i
\(364\) 5.22418i 0.273822i
\(365\) −8.25749 9.81900i −0.432217 0.513950i
\(366\) 0.744681 + 9.62265i 0.0389251 + 0.502984i
\(367\) 11.3139 + 11.3139i 0.590580 + 0.590580i 0.937788 0.347208i \(-0.112870\pi\)
−0.347208 + 0.937788i \(0.612870\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) −9.02856 + 1.40583i −0.470008 + 0.0731846i
\(370\) 0.390012 4.51489i 0.0202758 0.234718i
\(371\) 35.9830i 1.86814i
\(372\) −8.33431 7.13701i −0.432114 0.370037i
\(373\) −20.2494 + 20.2494i −1.04847 + 1.04847i −0.0497082 + 0.998764i \(0.515829\pi\)
−0.998764 + 0.0497082i \(0.984171\pi\)
\(374\) −0.913428 −0.0472322
\(375\) −11.0001 15.9373i −0.568041 0.823000i
\(376\) 0.282021 0.0145441
\(377\) 1.62584 1.62584i 0.0837349 0.0837349i
\(378\) 12.2516 + 7.57398i 0.630157 + 0.389563i
\(379\) 31.4641i 1.61620i −0.589042 0.808102i \(-0.700495\pi\)
0.589042 0.808102i \(-0.299505\pi\)
\(380\) −1.23665 + 14.3158i −0.0634387 + 0.734385i
\(381\) −24.3003 + 1.88056i −1.24494 + 0.0963438i
\(382\) 19.0413 + 19.0413i 0.974238 + 0.974238i
\(383\) −5.10098 5.10098i −0.260648 0.260648i 0.564669 0.825317i \(-0.309004\pi\)
−0.825317 + 0.564669i \(0.809004\pi\)
\(384\) −1.72689 + 0.133641i −0.0881249 + 0.00681983i
\(385\) −11.8565 14.0985i −0.604261 0.718529i
\(386\) 15.4597i 0.786878i
\(387\) 6.17302 + 4.50963i 0.313792 + 0.229237i
\(388\) 8.98748 8.98748i 0.456270 0.456270i
\(389\) 18.3647 0.931129 0.465565 0.885014i \(-0.345851\pi\)
0.465565 + 0.885014i \(0.345851\pi\)
\(390\) 5.20717 5.11493i 0.263675 0.259005i
\(391\) −0.307349 −0.0155433
\(392\) −0.483658 + 0.483658i −0.0244284 + 0.0244284i
\(393\) −5.45608 4.67226i −0.275223 0.235685i
\(394\) 2.79914i 0.141019i
\(395\) 32.1463 + 2.77691i 1.61746 + 0.139722i
\(396\) −1.37175 8.80970i −0.0689331 0.442704i
\(397\) −6.90089 6.90089i −0.346346 0.346346i 0.512401 0.858746i \(-0.328756\pi\)
−0.858746 + 0.512401i \(0.828756\pi\)
\(398\) 11.2354 + 11.2354i 0.563178 + 0.563178i
\(399\) 2.38055 + 30.7612i 0.119177 + 1.53998i
\(400\) 4.92593 + 0.857436i 0.246297 + 0.0428718i
\(401\) 18.3481i 0.916261i −0.888885 0.458131i \(-0.848519\pi\)
0.888885 0.458131i \(-0.151481\pi\)
\(402\) −14.9934 + 17.5087i −0.747803 + 0.873254i
\(403\) −8.44225 + 8.44225i −0.420538 + 0.420538i
\(404\) −3.00976 −0.149741
\(405\) −4.44613 19.6273i −0.220930 0.975290i
\(406\) 3.38190 0.167841
\(407\) −4.25896 + 4.25896i −0.211109 + 0.211109i
\(408\) 0.346258 0.404346i 0.0171423 0.0200181i
\(409\) 15.8713i 0.784783i 0.919798 + 0.392392i \(0.128352\pi\)
−0.919798 + 0.392392i \(0.871648\pi\)
\(410\) −5.21240 + 4.38348i −0.257422 + 0.216485i
\(411\) −1.26969 16.4067i −0.0626292 0.809285i
\(412\) 1.81831 + 1.81831i 0.0895816 + 0.0895816i
\(413\) 18.4838 + 18.4838i 0.909526 + 0.909526i
\(414\) −0.461565 2.96428i −0.0226847 0.145686i
\(415\) 29.4626 24.7772i 1.44626 1.21626i
\(416\) 1.88462i 0.0924013i
\(417\) −28.0620 24.0306i −1.37420 1.17679i
\(418\) 13.5043 13.5043i 0.660517 0.660517i
\(419\) −19.9035 −0.972349 −0.486175 0.873862i \(-0.661608\pi\)
−0.486175 + 0.873862i \(0.661608\pi\)
\(420\) 10.7355 + 0.0959261i 0.523838 + 0.00468071i
\(421\) −9.07200 −0.442142 −0.221071 0.975258i \(-0.570955\pi\)
−0.221071 + 0.975258i \(0.570955\pi\)
\(422\) −8.05445 + 8.05445i −0.392085 + 0.392085i
\(423\) −0.683180 0.499089i −0.0332173 0.0242666i
\(424\) 12.9809i 0.630407i
\(425\) −1.25689 + 0.884201i −0.0609682 + 0.0428901i
\(426\) 13.2104 1.02233i 0.640046 0.0495320i
\(427\) 10.9222 + 10.9222i 0.528561 + 0.528561i
\(428\) 10.1552 + 10.1552i 0.490872 + 0.490872i
\(429\) −9.67232 + 0.748525i −0.466984 + 0.0361391i
\(430\) 5.67695 + 0.490395i 0.273767 + 0.0236489i
\(431\) 6.60333i 0.318071i 0.987273 + 0.159036i \(0.0508384\pi\)
−0.987273 + 0.159036i \(0.949162\pi\)
\(432\) 4.41978 + 2.73231i 0.212647 + 0.131458i
\(433\) −2.95935 + 2.95935i −0.142217 + 0.142217i −0.774631 0.632414i \(-0.782064\pi\)
0.632414 + 0.774631i \(0.282064\pi\)
\(434\) −17.5607 −0.842941
\(435\) −3.31118 3.37089i −0.158759 0.161622i
\(436\) −3.22282 −0.154345
\(437\) 4.54391 4.54391i 0.217365 0.217365i
\(438\) −7.54831 6.46393i −0.360672 0.308858i
\(439\) 11.2528i 0.537068i −0.963270 0.268534i \(-0.913461\pi\)
0.963270 0.268534i \(-0.0865392\pi\)
\(440\) −4.27722 5.08605i −0.203909 0.242468i
\(441\) 2.02756 0.315709i 0.0965503 0.0150338i
\(442\) −0.409583 0.409583i −0.0194819 0.0194819i
\(443\) 16.2317 + 16.2317i 0.771194 + 0.771194i 0.978315 0.207122i \(-0.0664096\pi\)
−0.207122 + 0.978315i \(0.566410\pi\)
\(444\) −0.270842 3.49978i −0.0128536 0.166092i
\(445\) 0.472722 5.47236i 0.0224092 0.259415i
\(446\) 14.8040i 0.700989i
\(447\) 2.30622 2.69311i 0.109081 0.127380i
\(448\) −1.96010 + 1.96010i −0.0926061 + 0.0926061i
\(449\) 3.47861 0.164166 0.0820828 0.996626i \(-0.473843\pi\)
0.0820828 + 0.996626i \(0.473843\pi\)
\(450\) −10.4154 10.7944i −0.490985 0.508855i
\(451\) 9.05193 0.426239
\(452\) −3.72990 + 3.72990i −0.175440 + 0.175440i
\(453\) −2.97438 + 3.47336i −0.139749 + 0.163193i
\(454\) 22.8625i 1.07299i
\(455\) 1.00535 11.6383i 0.0471318 0.545611i
\(456\) 0.858785 + 11.0971i 0.0402163 + 0.519669i
\(457\) 24.5212 + 24.5212i 1.14705 + 1.14705i 0.987129 + 0.159925i \(0.0511251\pi\)
0.159925 + 0.987129i \(0.448875\pi\)
\(458\) 11.3347 + 11.3347i 0.529638 + 0.529638i
\(459\) −1.55436 + 0.366736i −0.0725511 + 0.0171178i
\(460\) −1.43919 1.71135i −0.0671028 0.0797921i
\(461\) 7.06441i 0.329022i 0.986375 + 0.164511i \(0.0526047\pi\)
−0.986375 + 0.164511i \(0.947395\pi\)
\(462\) −10.8382 9.28119i −0.504238 0.431800i
\(463\) 4.91698 4.91698i 0.228512 0.228512i −0.583559 0.812071i \(-0.698340\pi\)
0.812071 + 0.583559i \(0.198340\pi\)
\(464\) 1.22002 0.0566381
\(465\) 17.1935 + 17.5035i 0.797328 + 0.811705i
\(466\) 5.86409 0.271649
\(467\) −0.279235 + 0.279235i −0.0129214 + 0.0129214i −0.713538 0.700617i \(-0.752908\pi\)
0.700617 + 0.713538i \(0.252908\pi\)
\(468\) 3.33519 4.56539i 0.154169 0.211035i
\(469\) 36.8915i 1.70349i
\(470\) −0.628279 0.0542729i −0.0289804 0.00250342i
\(471\) 1.83407 0.141935i 0.0845093 0.00654003i
\(472\) 6.66802 + 6.66802i 0.306920 + 0.306920i
\(473\) −5.35515 5.35515i −0.246230 0.246230i
\(474\) 24.9187 1.92841i 1.14455 0.0885750i
\(475\) 5.50994 31.6544i 0.252813 1.45240i
\(476\) 0.851973i 0.0390501i
\(477\) 22.9721 31.4454i 1.05182 1.43978i
\(478\) −21.0475 + 21.0475i −0.962690 + 0.962690i
\(479\) 19.9714 0.912518 0.456259 0.889847i \(-0.349189\pi\)
0.456259 + 0.889847i \(0.349189\pi\)
\(480\) 3.87283 + 0.0346053i 0.176770 + 0.00157951i
\(481\) −3.81946 −0.174152
\(482\) 12.8377 12.8377i 0.584743 0.584743i
\(483\) −3.64682 3.12292i −0.165936 0.142098i
\(484\) 2.16749i 0.0985222i
\(485\) −21.7516 + 18.2925i −0.987691 + 0.830619i
\(486\) −5.87131 14.4405i −0.266328 0.655034i
\(487\) −1.40410 1.40410i −0.0636258 0.0636258i 0.674578 0.738204i \(-0.264326\pi\)
−0.738204 + 0.674578i \(0.764326\pi\)
\(488\) 3.94018 + 3.94018i 0.178363 + 0.178363i
\(489\) −1.24816 16.1286i −0.0564439 0.729360i
\(490\) 1.17056 0.984403i 0.0528803 0.0444708i
\(491\) 6.45884i 0.291483i −0.989323 0.145742i \(-0.953443\pi\)
0.989323 0.145742i \(-0.0465568\pi\)
\(492\) −3.43137 + 4.00701i −0.154698 + 0.180650i
\(493\) −0.265146 + 0.265146i −0.0119416 + 0.0119416i
\(494\) 12.1107 0.544887
\(495\) 1.36059 + 19.8900i 0.0611538 + 0.893989i
\(496\) −6.33502 −0.284451
\(497\) 14.9944 14.9944i 0.672593 0.672593i
\(498\) 19.3955 22.6492i 0.869132 1.01494i
\(499\) 9.53761i 0.426962i 0.976947 + 0.213481i \(0.0684802\pi\)
−0.976947 + 0.213481i \(0.931520\pi\)
\(500\) −10.8088 2.85813i −0.483386 0.127819i
\(501\) −0.992338 12.8228i −0.0443344 0.572883i
\(502\) −13.5208 13.5208i −0.603464 0.603464i
\(503\) −15.2096 15.2096i −0.678161 0.678161i 0.281423 0.959584i \(-0.409194\pi\)
−0.959584 + 0.281423i \(0.909194\pi\)
\(504\) 8.21699 1.27946i 0.366014 0.0569917i
\(505\) 6.70506 + 0.579206i 0.298371 + 0.0257743i
\(506\) 2.97195i 0.132119i
\(507\) 12.4300 + 10.6443i 0.552034 + 0.472730i
\(508\) −9.95020 + 9.95020i −0.441469 + 0.441469i
\(509\) 27.1370 1.20282 0.601412 0.798939i \(-0.294605\pi\)
0.601412 + 0.798939i \(0.294605\pi\)
\(510\) −0.849198 + 0.834157i −0.0376031 + 0.0369371i
\(511\) −15.9046 −0.703577
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 17.5580 28.4018i 0.775205 1.25397i
\(514\) 24.0535i 1.06096i
\(515\) −3.70085 4.40069i −0.163079 0.193918i
\(516\) 4.40057 0.340552i 0.193724 0.0149920i
\(517\) 0.592665 + 0.592665i 0.0260654 + 0.0260654i
\(518\) −3.97242 3.97242i −0.174538 0.174538i
\(519\) −39.5113 + 3.05771i −1.73435 + 0.134219i
\(520\) 0.362682 4.19851i 0.0159047 0.184117i
\(521\) 41.9658i 1.83855i 0.393611 + 0.919277i \(0.371226\pi\)
−0.393611 + 0.919277i \(0.628774\pi\)
\(522\) −2.95543 2.15906i −0.129356 0.0944994i
\(523\) 22.7710 22.7710i 0.995704 0.995704i −0.00428643 0.999991i \(-0.501364\pi\)
0.999991 + 0.00428643i \(0.00136442\pi\)
\(524\) −4.14724 −0.181173
\(525\) −23.8978 2.27967i −1.04298 0.0994928i
\(526\) −17.4761 −0.761992
\(527\) 1.37678 1.37678i 0.0599736 0.0599736i
\(528\) −3.90988 3.34819i −0.170156 0.145711i
\(529\) 1.00000i 0.0434783i
\(530\) 2.49807 28.9184i 0.108509 1.25614i
\(531\) −4.35256 27.9532i −0.188885 1.21306i
\(532\) 12.5957 + 12.5957i 0.546094 + 0.546094i
\(533\) 4.05891 + 4.05891i 0.175811 + 0.175811i
\(534\) −0.328279 4.24198i −0.0142060 0.183568i
\(535\) −20.6693 24.5779i −0.893610 1.06259i
\(536\) 13.3086i 0.574844i
\(537\) 14.2049 16.5879i 0.612986 0.715820i
\(538\) −14.2128 + 14.2128i −0.612758 + 0.612758i
\(539\) −2.03280 −0.0875591
\(540\) −9.32045 6.93752i −0.401088 0.298543i
\(541\) 8.43337 0.362579 0.181290 0.983430i \(-0.441973\pi\)
0.181290 + 0.983430i \(0.441973\pi\)
\(542\) 19.7054 19.7054i 0.846419 0.846419i
\(543\) −1.97584 + 2.30730i −0.0847912 + 0.0990157i
\(544\) 0.307349i 0.0131775i
\(545\) 7.17971 + 0.620208i 0.307545 + 0.0265668i
\(546\) −0.698164 9.02157i −0.0298787 0.386088i
\(547\) −13.9532 13.9532i −0.596597 0.596597i 0.342808 0.939405i \(-0.388622\pi\)
−0.939405 + 0.342808i \(0.888622\pi\)
\(548\) −6.71805 6.71805i −0.286981 0.286981i
\(549\) −2.57196 16.5177i −0.109769 0.704959i
\(550\) 8.54990 + 12.1537i 0.364569 + 0.518235i
\(551\) 7.83994i 0.333993i
\(552\) −1.31559 1.12660i −0.0559953 0.0479511i
\(553\) 28.2839 28.2839i 1.20275 1.20275i
\(554\) −9.96921 −0.423551
\(555\) −0.0701326 + 7.84883i −0.00297696 + 0.333164i
\(556\) −21.3303 −0.904607
\(557\) −19.9924 + 19.9924i −0.847106 + 0.847106i −0.989771 0.142665i \(-0.954433\pi\)
0.142665 + 0.989771i \(0.454433\pi\)
\(558\) 15.3462 + 11.2110i 0.649657 + 0.474600i
\(559\) 4.80252i 0.203125i
\(560\) 4.74387 3.98945i 0.200465 0.168585i
\(561\) 1.57739 0.122071i 0.0665974 0.00515386i
\(562\) −11.1642 11.1642i −0.470934 0.470934i
\(563\) −31.0332 31.0332i −1.30789 1.30789i −0.922935 0.384957i \(-0.874216\pi\)
−0.384957 0.922935i \(-0.625784\pi\)
\(564\) −0.487019 + 0.0376896i −0.0205072 + 0.00158702i
\(565\) 9.02716 7.59158i 0.379776 0.319380i
\(566\) 18.6737i 0.784912i
\(567\) −22.1694 11.4421i −0.931027 0.480522i
\(568\) 5.40925 5.40925i 0.226967 0.226967i
\(569\) −30.3632 −1.27289 −0.636447 0.771321i \(-0.719596\pi\)
−0.636447 + 0.771321i \(0.719596\pi\)
\(570\) 0.222376 24.8870i 0.00931431 1.04240i
\(571\) −13.6437 −0.570973 −0.285486 0.958383i \(-0.592155\pi\)
−0.285486 + 0.958383i \(0.592155\pi\)
\(572\) −3.96052 + 3.96052i −0.165598 + 0.165598i
\(573\) −35.4269 30.3375i −1.47998 1.26737i
\(574\) 8.44292i 0.352401i
\(575\) 2.87686 + 4.08946i 0.119973 + 0.170542i
\(576\) 2.96428 0.461565i 0.123512 0.0192319i
\(577\) 29.2454 + 29.2454i 1.21750 + 1.21750i 0.968503 + 0.249001i \(0.0801021\pi\)
0.249001 + 0.968503i \(0.419898\pi\)
\(578\) −11.9540 11.9540i −0.497222 0.497222i
\(579\) 2.06605 + 26.6972i 0.0858620 + 1.10950i
\(580\) −2.71793 0.234784i −0.112856 0.00974888i
\(581\) 47.7228i 1.97988i
\(582\) −14.3193 + 16.7215i −0.593553 + 0.693127i
\(583\) −27.2791 + 27.2791i −1.12979 + 1.12979i
\(584\) −5.73758 −0.237423
\(585\) −8.30862 + 9.52880i −0.343519 + 0.393968i
\(586\) −9.81215 −0.405336
\(587\) −30.7364 + 30.7364i −1.26863 + 1.26863i −0.321830 + 0.946798i \(0.604298\pi\)
−0.946798 + 0.321830i \(0.895702\pi\)
\(588\) 0.770587 0.899860i 0.0317785 0.0371096i
\(589\) 40.7093i 1.67740i
\(590\) −13.5716 16.1380i −0.558734 0.664392i
\(591\) 0.374079 + 4.83380i 0.0153876 + 0.198836i
\(592\) −1.43305 1.43305i −0.0588980 0.0588980i
\(593\) 24.9741 + 24.9741i 1.02557 + 1.02557i 0.999665 + 0.0259005i \(0.00824531\pi\)
0.0259005 + 0.999665i \(0.491755\pi\)
\(594\) 3.54620 + 15.0300i 0.145502 + 0.616690i
\(595\) −0.163956 + 1.89800i −0.00672154 + 0.0778105i
\(596\) 2.04707i 0.0838514i
\(597\) −20.9037 17.9007i −0.855531 0.732627i
\(598\) −1.33263 + 1.33263i −0.0544953 + 0.0544953i
\(599\) 35.3695 1.44516 0.722579 0.691288i \(-0.242956\pi\)
0.722579 + 0.691288i \(0.242956\pi\)
\(600\) −8.62112 0.822390i −0.351956 0.0335739i
\(601\) 36.5041 1.48903 0.744517 0.667604i \(-0.232680\pi\)
0.744517 + 0.667604i \(0.232680\pi\)
\(602\) 4.99486 4.99486i 0.203575 0.203575i
\(603\) 23.5521 32.2393i 0.959114 1.31288i
\(604\) 2.64015i 0.107426i
\(605\) −0.417117 + 4.82867i −0.0169582 + 0.196313i
\(606\) 5.19752 0.402227i 0.211135 0.0163394i
\(607\) 22.0917 + 22.0917i 0.896673 + 0.896673i 0.995140 0.0984669i \(-0.0313939\pi\)
−0.0984669 + 0.995140i \(0.531394\pi\)
\(608\) 4.54391 + 4.54391i 0.184280 + 0.184280i
\(609\) −5.84017 + 0.451961i −0.236656 + 0.0183144i
\(610\) −8.01956 9.53607i −0.324702 0.386104i
\(611\) 0.531504i 0.0215024i
\(612\) −0.543912 + 0.744535i −0.0219863 + 0.0300960i
\(613\) 16.7926 16.7926i 0.678246 0.678246i −0.281357 0.959603i \(-0.590784\pi\)
0.959603 + 0.281357i \(0.0907845\pi\)
\(614\) 11.8644 0.478808
\(615\) 8.41542 8.26636i 0.339343 0.333332i
\(616\) −8.23826 −0.331929
\(617\) 26.9980 26.9980i 1.08690 1.08690i 0.0910505 0.995846i \(-0.470978\pi\)
0.995846 0.0910505i \(-0.0290225\pi\)
\(618\) −3.38301 2.89701i −0.136085 0.116535i
\(619\) 31.5835i 1.26945i 0.772739 + 0.634724i \(0.218886\pi\)
−0.772739 + 0.634724i \(0.781114\pi\)
\(620\) 14.1130 + 1.21913i 0.566791 + 0.0489614i
\(621\) 1.19322 + 5.05729i 0.0478823 + 0.202942i
\(622\) −16.0579 16.0579i −0.643865 0.643865i
\(623\) −4.81485 4.81485i −0.192903 0.192903i
\(624\) −0.251863 3.25453i −0.0100826 0.130286i
\(625\) 23.5296 + 8.44734i 0.941184 + 0.337894i
\(626\) 26.9989i 1.07909i
\(627\) −21.5157 + 25.1251i −0.859254 + 1.00340i
\(628\) 0.750993 0.750993i 0.0299679 0.0299679i
\(629\) 0.622887 0.0248361
\(630\) −18.5518 + 1.26905i −0.739121 + 0.0505600i
\(631\) −27.4404 −1.09239 −0.546193 0.837659i \(-0.683924\pi\)
−0.546193 + 0.837659i \(0.683924\pi\)
\(632\) 10.2034 10.2034i 0.405870 0.405870i
\(633\) 12.8327 14.9855i 0.510055 0.595622i
\(634\) 0.0389545i 0.00154708i
\(635\) 24.0816 20.2519i 0.955650 0.803673i
\(636\) −1.73477 22.4165i −0.0687883 0.888872i
\(637\) −0.911514 0.911514i −0.0361155 0.0361155i
\(638\) 2.56386 + 2.56386i 0.101504 + 0.101504i
\(639\) −22.6762 + 3.53090i −0.897058 + 0.139680i
\(640\) 1.71135 1.43919i 0.0676470 0.0568892i
\(641\) 1.78898i 0.0706606i −0.999376 0.0353303i \(-0.988752\pi\)
0.999376 0.0353303i \(-0.0112483\pi\)
\(642\) −18.8941 16.1798i −0.745691 0.638566i
\(643\) 24.6839 24.6839i 0.973437 0.973437i −0.0262188 0.999656i \(-0.508347\pi\)
0.999656 + 0.0262188i \(0.00834667\pi\)
\(644\) −2.77200 −0.109232
\(645\) −9.86899 0.0881836i −0.388591 0.00347222i
\(646\) −1.97505 −0.0777072
\(647\) 2.36727 2.36727i 0.0930671 0.0930671i −0.659040 0.752108i \(-0.729037\pi\)
0.752108 + 0.659040i \(0.229037\pi\)
\(648\) −7.99761 4.12773i −0.314176 0.162153i
\(649\) 28.0255i 1.10010i
\(650\) −1.61594 + 9.28353i −0.0633826 + 0.364130i
\(651\) 30.3254 2.34683i 1.18854 0.0919794i
\(652\) −6.60415 6.60415i −0.258639 0.258639i
\(653\) 2.10868 + 2.10868i 0.0825189 + 0.0825189i 0.747161 0.664643i \(-0.231416\pi\)
−0.664643 + 0.747161i \(0.731416\pi\)
\(654\) 5.56545 0.430701i 0.217626 0.0168417i
\(655\) 9.23911 + 0.798106i 0.361002 + 0.0311846i
\(656\) 3.04579i 0.118918i
\(657\) 13.8989 + 10.1537i 0.542249 + 0.396134i
\(658\) −0.552791 + 0.552791i −0.0215500 + 0.0215500i
\(659\) 40.8784 1.59240 0.796199 0.605035i \(-0.206841\pi\)
0.796199 + 0.605035i \(0.206841\pi\)
\(660\) 8.06598 + 8.21143i 0.313968 + 0.319629i
\(661\) 17.8125 0.692828 0.346414 0.938082i \(-0.387399\pi\)
0.346414 + 0.938082i \(0.387399\pi\)
\(662\) −0.743610 + 0.743610i −0.0289012 + 0.0289012i
\(663\) 0.762041 + 0.652567i 0.0295952 + 0.0253436i
\(664\) 17.2160i 0.668111i
\(665\) −25.6365 30.4844i −0.994140 1.18213i
\(666\) 0.935427 + 6.00753i 0.0362471 + 0.232787i
\(667\) 0.862686 + 0.862686i 0.0334033 + 0.0334033i
\(668\) −5.25056 5.25056i −0.203150 0.203150i
\(669\) 1.97842 + 25.5648i 0.0764900 + 0.988392i
\(670\) 2.56114 29.6485i 0.0989455 1.14542i
\(671\) 16.5605i 0.639310i
\(672\) 3.12292 3.64682i 0.120469 0.140679i
\(673\) 13.7420 13.7420i 0.529714 0.529714i −0.390773 0.920487i \(-0.627792\pi\)
0.920487 + 0.390773i \(0.127792\pi\)
\(674\) 14.1764 0.546054
\(675\) 19.4288 + 17.2489i 0.747813 + 0.663909i
\(676\) 9.44819 0.363392
\(677\) 1.91031 1.91031i 0.0734192 0.0734192i −0.669444 0.742863i \(-0.733467\pi\)
0.742863 + 0.669444i \(0.233467\pi\)
\(678\) 5.94265 6.93959i 0.228226 0.266513i
\(679\) 35.2328i 1.35211i
\(680\) −0.0591471 + 0.684704i −0.00226819 + 0.0262572i
\(681\) 3.05537 + 39.4810i 0.117082 + 1.51292i
\(682\) −13.3130 13.3130i −0.509780 0.509780i
\(683\) −33.5563 33.5563i −1.28400 1.28400i −0.938374 0.345623i \(-0.887668\pi\)
−0.345623 0.938374i \(-0.612332\pi\)
\(684\) −2.96605 19.0487i −0.113410 0.728344i
\(685\) 13.6735 + 16.2591i 0.522436 + 0.621229i
\(686\) 17.5080i 0.668458i
\(687\) −21.0886 18.0590i −0.804581 0.688996i
\(688\) 1.80190 1.80190i 0.0686966 0.0686966i
\(689\) −24.4641 −0.932006
\(690\) 2.71403 + 2.76297i 0.103322 + 0.105185i
\(691\) −27.4000 −1.04234 −0.521172 0.853451i \(-0.674505\pi\)
−0.521172 + 0.853451i \(0.674505\pi\)
\(692\) −16.1787 + 16.1787i −0.615020 + 0.615020i
\(693\) 19.9567 + 14.5791i 0.758092 + 0.553816i
\(694\) 25.8642i 0.981790i
\(695\) 47.5191 + 4.10486i 1.80250 + 0.155706i
\(696\) −2.10684 + 0.163045i −0.0798596 + 0.00618020i
\(697\) −0.661937 0.661937i −0.0250727 0.0250727i
\(698\) 20.2968 + 20.2968i 0.768247 + 0.768247i
\(699\) −10.1266 + 0.783682i −0.383024 + 0.0296416i
\(700\) −11.3360 + 7.97466i −0.428460 + 0.301414i
\(701\) 17.7628i 0.670893i −0.942059 0.335446i \(-0.891113\pi\)
0.942059 0.335446i \(-0.108887\pi\)
\(702\) −5.14938 + 8.32963i −0.194351 + 0.314381i
\(703\) −9.20888 + 9.20888i −0.347319 + 0.347319i
\(704\) −2.97195 −0.112010
\(705\) 1.09222 + 0.00975945i 0.0411354 + 0.000367562i
\(706\) −14.7901 −0.556631
\(707\) 5.89944 5.89944i 0.221871 0.221871i
\(708\) −12.4060 10.6238i −0.466247 0.399267i
\(709\) 25.1030i 0.942763i 0.881929 + 0.471382i \(0.156245\pi\)
−0.881929 + 0.471382i \(0.843755\pi\)
\(710\) −13.0915 + 11.0096i −0.491316 + 0.413183i
\(711\) −42.7740 + 6.66031i −1.60415 + 0.249781i
\(712\) −1.73696 1.73696i −0.0650953 0.0650953i
\(713\) −4.47954 4.47954i −0.167760 0.167760i
\(714\) 0.113858 + 1.47126i 0.00426104 + 0.0550606i
\(715\) 9.58530 8.06095i 0.358470 0.301463i
\(716\) 12.6087i 0.471209i
\(717\) 33.5338 39.1594i 1.25234 1.46244i
\(718\) 7.38357 7.38357i 0.275552 0.275552i
\(719\) 7.11858 0.265478 0.132739 0.991151i \(-0.457623\pi\)
0.132739 + 0.991151i \(0.457623\pi\)
\(720\) −6.69256 + 0.457809i −0.249417 + 0.0170615i
\(721\) −7.12813 −0.265466
\(722\) 15.7644 15.7644i 0.586692 0.586692i
\(723\) −20.4537 + 23.8850i −0.760681 + 0.888292i
\(724\) 1.75381i 0.0651799i
\(725\) 6.00975 + 1.04609i 0.223196 + 0.0388508i
\(726\) 0.289665 + 3.74301i 0.0107505 + 0.138916i
\(727\) −21.0233 21.0233i −0.779711 0.779711i 0.200070 0.979782i \(-0.435883\pi\)
−0.979782 + 0.200070i \(0.935883\pi\)
\(728\) −3.69405 3.69405i −0.136911 0.136911i
\(729\) 12.0689 + 24.1524i 0.446998 + 0.894535i
\(730\) 12.7820 + 1.10415i 0.473083 + 0.0408666i
\(731\) 0.783208i 0.0289680i
\(732\) −7.33081 6.27767i −0.270955 0.232030i
\(733\) −8.70985 + 8.70985i −0.321706 + 0.321706i −0.849421 0.527715i \(-0.823049\pi\)
0.527715 + 0.849421i \(0.323049\pi\)
\(734\) −16.0003 −0.590580
\(735\) −1.88986 + 1.85639i −0.0697086 + 0.0684739i
\(736\) −1.00000 −0.0368605
\(737\) −27.9679 + 27.9679i −1.03021 + 1.03021i
\(738\) 5.39009 7.37823i 0.198412 0.271596i
\(739\) 13.3134i 0.489743i −0.969556 0.244871i \(-0.921254\pi\)
0.969556 0.244871i \(-0.0787458\pi\)
\(740\) 2.91673 + 3.46829i 0.107221 + 0.127497i
\(741\) −20.9138 + 1.61849i −0.768289 + 0.0594566i
\(742\) −25.4438 25.4438i −0.934072 0.934072i
\(743\) −31.8345 31.8345i −1.16789 1.16789i −0.982702 0.185193i \(-0.940709\pi\)
−0.185193 0.982702i \(-0.559291\pi\)
\(744\) 10.9399 0.846618i 0.401075 0.0310385i
\(745\) −0.393944 + 4.56041i −0.0144330 + 0.167081i
\(746\) 28.6369i 1.04847i
\(747\) −30.4669 + 41.7047i −1.11473 + 1.52590i
\(748\) 0.645891 0.645891i 0.0236161 0.0236161i
\(749\) −39.8106 −1.45465
\(750\) 19.0476 + 3.49117i 0.695521 + 0.127479i
\(751\) 1.87068 0.0682622 0.0341311 0.999417i \(-0.489134\pi\)
0.0341311 + 0.999417i \(0.489134\pi\)
\(752\) −0.199419 + 0.199419i −0.00727207 + 0.00727207i
\(753\) 25.1559 + 21.5420i 0.916732 + 0.785035i
\(754\) 2.29928i 0.0837349i
\(755\) 0.508077 5.88165i 0.0184908 0.214055i
\(756\) −14.0188 + 3.30761i −0.509860 + 0.120297i
\(757\) −4.50446 4.50446i −0.163717 0.163717i 0.620494 0.784211i \(-0.286932\pi\)
−0.784211 + 0.620494i \(0.786932\pi\)
\(758\) 22.2485 + 22.2485i 0.808102 + 0.808102i
\(759\) −0.397175 5.13223i −0.0144165 0.186288i
\(760\) −9.24836 10.9972i −0.335473 0.398912i
\(761\) 29.5482i 1.07112i −0.844497 0.535561i \(-0.820100\pi\)
0.844497 0.535561i \(-0.179900\pi\)
\(762\) 15.8531 18.5126i 0.574298 0.670642i
\(763\) 6.31706 6.31706i 0.228693 0.228693i
\(764\) −26.9285 −0.974238
\(765\) 1.35499 1.55398i 0.0489898 0.0561843i
\(766\) 7.21387 0.260648
\(767\) −12.5667 + 12.5667i −0.453757 + 0.453757i
\(768\) 1.12660 1.31559i 0.0406525 0.0474723i
\(769\) 14.7558i 0.532107i 0.963958 + 0.266054i \(0.0857199\pi\)
−0.963958 + 0.266054i \(0.914280\pi\)
\(770\) 18.3530 + 1.58539i 0.661395 + 0.0571336i
\(771\) −3.21454 41.5378i −0.115769 1.49595i
\(772\) 10.9317 + 10.9317i 0.393439 + 0.393439i
\(773\) 9.22983 + 9.22983i 0.331974 + 0.331974i 0.853336 0.521362i \(-0.174576\pi\)
−0.521362 + 0.853336i \(0.674576\pi\)
\(774\) −7.55377 + 1.17619i −0.271515 + 0.0422773i
\(775\) −31.2059 5.43188i −1.12095 0.195119i
\(776\) 12.7102i 0.456270i
\(777\) 7.39080 + 6.32905i 0.265144 + 0.227053i